Combine the milk, cinnamon stick, and whole cloves in a medium saucepan. Bring to a bare simmer over medium heat, remove from the heat, and steep for 10 minutes.

Add the cubed sweet potato and enough water to just cover. Simmer over medium heat for 12 to 15 minutes, until a fork slides through with no resistance.

Remove the cinnamon stick and cloves. Drain, reserving 2 tablespoons of the cooking liquid, then mash the sweet potato completely smooth.

Return the mash to the pan over low heat and stir in the flour all at once. Stir for 2 to 3 minutes, until the mixture pulls away from the sides and forms a rough ball.

Scrape the dough into a bowl and cool for 10 minutes. Beat in the whole egg, then the yolks one at a time, until the dough holds a soft peak. Loosen with the reserved cooking liquid if needed.

Heat 2 inches of oil in a heavy pot to 360 degrees F.

Transfer the dough to a piping bag fitted with a large open star tip. Pipe 3-inch lengths over the oil and snip them off with kitchen shears.

Fry 4 or 5 at a time for 3 to 4 minutes, turning once, until the ridges are dark gold and crisp. Drain on a wire rack.

Whisk the sugar and ground cinnamon in a shallow dish and roll each churro while it is still hot.

Warm the cream until bubbles form at the edge, then pour it over the chopped chocolate and let it sit for 2 minutes.

Whisk in the cocoa powder and salt until glossy and smooth. Thin with a tablespoon of warm milk if the sauce is too thick. Serve warm alongside the churros.